1. Data types

This module will cover:

assigning objects
data structure and syntax
troubleshooting through Rstudio
data subsetting

`R` Objects

Everything in R is an object. But what does this mean to someone who doesn’t have a computer science background?

R doesn’t let users directly access the computer’s memory, instead users access many different specialized data structures. You can think of this design as a filing cabinet. One drawer contains textbooks, another pictures, another data tables, and so on. In this analogy, each drawer is a different object class.

If we look in the textbook drawer, each book or object has a similar structure (front cover, title page, table of contents, etc.). Just like each book has a unique title, R objects have user assigned names.

Objects in R are often assigned a name by using an arrow made from a the less than sign and dash <-

myname <- "Odum" #this line assigns "Odum" to an object 'myname'
myname #print the content of 'myname' object by running it in the console

The information in the object is retrived by calling the object’s name.

Data types

One of the first concepts we’ll need to understand how R organizes information. This is very important because nearly every task requires manipulating data. R has 5 basic (‘atomic’) classes :

logical (TRUE, FALSE)
character (“blue”, “purple”)
integer (1,2,3) each number must be followed by L
numeric (1,1.5,2)
complex (i)

Concept Check: What is the class of myname?

Based on the decsription above, we can guess that is should be a character. We can use a few base R functions to get information about objects. Some helpful functions include:

typeof()
length()
attributes()
str()

Practice: Verify myname class type and determine the length. You may need to pull up the documentation page for the functions.

#What is the class
?typeof() #look up documentation for typeof()
typeof(myname) #return the object type of "myname"

#How long is the object
?length()
length(myname)

This object has a length of one. Why?

Let’s make an numeric class object with a length greater than 1

y <- c(1:10) #colon indicates '1 to 10' 
typeof(y)
length(y)
attributes(y)

Concept Check: How could we make myname longer than 1?

Data Structure

These 5 classes or modes can then be combind to create many different types of data structure. Common data structures include:

vector
matrix
list
factors
data frame

These data structures can consist of either a single class or a mixture of data types. Let’s look at examples of each type.

Vectors

Vectors are the most common data structure. Vectors (the R data ) are vectors of elements can be character, logical, numeric or integer class.

#concatenating objects into a vector using "c"
character_vector <- c("a", "b", "c")
numeric_vector <- c(1, 10, 49)
boolean_vector <- c("TRUE", "FALSE", "TRUE")

You can creating vectors using handy functions

vec1 <-  rep(1:4, 2)
vec2 <- rep(1:4, each = 2) 
vec3<-seq(1, 15, by = 2)

You can transform and use operators to create other vectors.

Practice: Explore the difference between vec4 and vec5. How was the addition done in both cases?

vec4<-vec1+vec2+vec3

vec5<-sum(vec1,vec2,vec3)

There are many different ways to manipulate vectors. These methods will come in handy when exploring and plotting data. Accessing specific elements in the vector can be done based on the value of the element or the element location in the string.

Practice: Determine how the command accesses the vector. Complete the comment where needed.

vec4[1] # first elements

vec4[1:3] # # What happened here?

vec4[c(1,2,4)] # first second and fourth elements

vec6 <- c(1:20) #creating a vector 

x <- c(3, 5, 12) # creating another vector 

vec6[x]# the elements of vec6 that coicinde with vector x

vec6[-x] # What happened here?

vec7 <- c(1:5,2,2,2,2,2) #creating a vector 

vec7[vec7 > 4] # elements bigger than 4

vec7[vec7 < 4] # # What happened here?

which(vec7 < 4) # positions

which(vec7 == 2) # position

Matrices

Matrices are a special type of vector. The data is organized into columns and rows giving the matrix dimensions. There are many ways to make a matrix, but the default is to fill column-wise.

rnames <- c("R1", "R2")
cnames <- c("C1", "C2")
m<-matrix(data = NA, nrow = 2, ncol = 2, byrow=TRUE,
  dimnames=list(rnames, cnames))

Practice: Add more rows and columns to the matrix and fill it with 1s and change the names of rows and columns

m<-matrix(data = , nrow = , ncol = , byrow = TRUE, dimnames = list(rnames, cnames))

Another way to build a matrix is to combine vectors by rows (rbind) or columns (cbind)

m1<-rbind(vec1,vec2)
m2<-cbind(vec2,vec3,vec4)

Subsetting from a matrix. Note that here we use two values for subsetting.

# All elements in first row of m1
m1[1,]

#All elements in first column of m1

m1[,1]

Practice: Write the command that is descibed in the comments.

# All elements in second row of m2


#All elements in third column of m2


#The elements in the bottom 2 rows, and the second and third column of m2

Lists

Lists are really containers for vectors and matrices. They can hold different data classes in each entry of the list including lists! This means you can make lists of lists, which is why lists are considered a recursive vector.

#make a list
w <- list(name="Odum", mynumbers=vec1, mymatrix=m, age=5.3)
primes <- list(
    2, 3, 4:5,
    6:7, 8:11, 12:13,
    14:17, 18:19, 20:23)

Practice: Follow comments to interact with the list

#check the class of an entry

#determine the structure of w 

#subsetting 

w[[2]] ## what is this?
w[[2]][1] #what is this? How is it different than last command?

Factors

Factors are used for ordered or unordered categorical data. This data type is important for modeling and plotting work. Factors can only contain pre-defined values and are really a way at add labels to integers.

order categories: low,med, high unorder categories: blue, red

dat<-c('low','med', 'high')

# check if it is a factor
print(is.factor(dat))

#Making the vector a into a factor

factor_dat <- factor(dat)

#check again


#Changing the order
new_order_dat <- factor(factor_dat,levels = c("med","high","low"))

Practice: Making a vector into a factor

hues <- c(rep("blue",20), rep("red", 30)) 
# make hues a factor

#summarize hues
summary(hues)

Data frames

Data frames are the most common way we organize ecological data. They have the freedom of lists and the organization of a matrix. Each column can be a different data class. This means for a single observation or row in a data frame categorical, numeric, factorial, etc. can be included.

# creating vectors
 n = c(2, 3, 5) 
 s = c("aa", "bb", "cc") 
 b = c(TRUE, FALSE, TRUE) 
 # creating the data frame
 df = data.frame(n, s, b)
 
names(df) <- c("ID","Code","Passed") # variable names

Like with the matrix we can subset a data frame

# subsetting a column
df[,1]

# subsetting a row
df[1,] 

# the $ for subsetting

df$ID

Useful functions

head() - see first 6 rows
tail() - see last 6 rows
dim() - see dimensions
nrow() - number of rows
ncol() - number of columns
str() - structure of each column
names() - will list the names attribute for a data frame (or any object really), which gives the column names.

Going further

The R community lead by Garrett Grolemund and Hadley Wickham has developed work flows that are more efficient for common data science manipulations. Check out the Tidyverse and R for Data Science.

In general, if you’re searching for a quick reference for R statmethods is a good source.

2. Writing a script

This module will cover:

script best practices

The importance of a script

Permanent

Repeatable

Annotated

Shareable

Practice: We will do this exercise together…

Step 1

File --> New File --> R Script or Top left green and white plus sign drop down then select R Script

Step 2

The # symbols declares that anything after it is a comment

You should start with some information at the top, for example:
#############################
## Author:                ###
## Date:                  ###
## Purpose:               ###
#############################

Step 3

Leave an empty “blank line” - These are important to create chunks of code and annotation

Step 4

Next if your script has code that is standalone and independent, we recomend you always start a script by clearing R’s brain rm(list=ls())

If your script is a function or group of functions to be sourced by another script, skip this step!!

Try typing the rm function instead of copy pasting it. You will notice Rstudio closes brackets for you automatically

Step 5

Leave another empty “blank line”

Step 6

Now you are ready to start writing your first script! Copy paste the code inside the [] Then move to Step 7

We will go over how to construct these functions in the next module

Practice:Lets try to understnd what this loop does

 for(i in 1:10){ # for loop run from 1 to 10
print("Darwin rules!") # write a sentence 10 times
print(i*i) # also print each number multiplied by itself 
}

Practice: Annotate the function

Isit <- function(x){
 if (x == 10)
 print("It's a ten!")
 else print("Not a ten!")
}


Isit(10)

Isit(1)

Practice: Annotate the rest of the function and plot

# A simple function that needs functions from the ape library to run
# ape is a library of functions for analysis of evolutionary relationships:
Tree <- function(x){
   #this function creates a plot of a random evolutionary tree
   #of size x
   require(ape)
   tree <- rcoal(x)
   plot(tree)
 }
Tree(30)

Check: Notice the colours in your script, this is syntax highlighting. Separates:

comments

R functions

numbers

other things

Step 7

Once you are done writing your script and you are happy with the commenting. Save it in your working directory of your project. Give it a meaningful name.

Step 8

Practice: Open your script and run it!

File --> Open file --> Search for your working directory then run all or parts of it

Or you can double click on your R script open it in R studio and run specific parts of it

Mac: cmd+return 
Windows: ctrl+enter
or pressing Run

setwd("your path") # sets your working directory. You can also do this mannually
source("Script1.R") # source your script, rename accordingly

Step 9

In this settingm it’s a good idea to create a README text file that describes your project and keep it in the project folder.

This file should describe the overall project and the files in the project folder

Practice: Create a README text file

File --> New File --> Text file 

Save it using the name README.txt" in the same directory of your project

Going further

Rmarkdown for using a productive notebook interface to weave together narrative text and code to produce elegantly formatted output

3. Functions

This module will cover:

function syntax
control statements
logic statements

which will require the following skills already covered:

data structure
assigning an object

What is a function

Functions incorporate sets of instructions that you want to use repeatedly or that, because of their complexity, are better self-contained in a script and called when needed.

You can write your own functions, but R and its packages come with “pre-made” functions as well.

A useful function is rm(list=ls()), which clears R’s brain.

Others include seq(), log(), sin()…

A typical function has the follwoing architecture

func.name = function (arglist)  {body}

Practice: Let’s copy and paste them into the console

Example 1a: Simple function

my.function1<-function(a,b,c){
 tmp<-a+b
 tmp2<-tmp/c
 return(tmp2)
}

#Using this function we have:
 out1<-my.function1(4,7,2)
 out1

Practice: Choose other sets of numbers

out2<-my.function1(,,)
out2

Practice: Create a function that will return the sum of 2 integers

Example 1b: Rounding function

Roundme <- function(x){
   #this function uses the floor function to 
   #do what the round function does
   x <- x+0.5
   floor(x)
 }

Example 2a: Control statements if

x <- 8

if (x < 9) print("x is less than nine")
 
x <- 10

if (x < 9) print("x is less than nine")

Example 2b: Control statements if else

 a<-5
 if(a<1){
 b<-5
 c<-4
 } else {
 b<-10
 }
 b

Practice: Uncomment and fill in a simple function with a nested if statement will print alternative outcomes

#Isit <- function(x){
# if (x == ??)
 #print("???!")
 #else print("???")
#}


#Isit(?)

#Isit(?)

Example 2c: Control statements while

x <- 2
while(x < 10){
 print(x)
 x <- x+1
}

print("The end")

Example 3: for loop

a<-c() # creating an empty vector
 for(i in 1:10){ # i becomes 1 through 10 iteratively 
a[i]<-i^3  # this is the operation
 }
 a # seeing what the vector a becomes

Example 4: Random number generation

Here is an example, there are a number of distributions available

random_numbers<-rnorm(3,mean=5,sd=3) # normal distribution generates 3 numbers with a mean and a sd
random_numbers

Example 5: Descriptive stats

dat<-rnorm(30,mean=5,sd=3) # creating a vector

dat # check it

sort (dat) #sort vector

unique (dat) #unique values

max(dat) #max

min(dat) #min

mean(dat) # taking the mean

sum(dat) # sum the vector elements

var(dat) # taking the variance

length(dat) # length of vector

sqrt(var(dat)/length(dat)) # standard error

Practice: Write a function to compute standard error of dat

Example 6: The apply function

apply are functions to manipulate slices of data from matrices, arrays, lists and data frames in a repetitive way

X <- matrix(rnorm(30), nrow=5, ncol=6) # creating a matrix

# Sum the values of each column with `apply()`
apply(X, 2, sum)

Practice: How do you calculate the sum of each row using apply?

Example 7: The lapply function

lapply applies a given function to every element of a list and obtain a list as result

# create a list with 2 elements
l <- list(a = 1:10, b = 11:20)

# the mean of the values in each element
lapply(l, mean)

# the sum of the values in each element
lapply(l, sum)

Example 8: The sapply function

sapply will return either a vector, with elements [[‘a’]] and [[‘b’]], or a matrix with column names “a” and “b”

# create a list with 2 elements
l <- list(a = 1:10, b = 11:20)
# mean of values using sapply
l.mean <- sapply(l, mean)
# what type of object was returned?
class(l.mean)

# it's a numeric vector, so we can get element "a" like this
l.mean[['a']]

Going further

rapply, tapply, parallel computing in R (https://www.r-bloggers.com/how-to-go-parallel-in-r-basics-tips/)

4. Manipulating & exploring data

This module will cover:

loading data
calculate simple stats in base R
plot function in base R

which will require the following skills already covered:

logic statements
manipulating data
assigning an object

Loading tabular data

Before we jump into calculating summary statistics and simple data visualization, we need to import or load data into R. External data, often in table form, needs to be loaded into R. Common ways to read data frames into R uses read.csv or read.table.

Practice: Write code to load a .csv file into R. How does R know where the file is located?

There are lots of tricks to loading data depending on the data types. For more information check out Datacamp’s tutorial.

Iterative process of data exploration

Data exploration is a key step in scientific inquiry. Effective exploration might include transforming the data by grouping replicate populatons, calculating summary statistics, etc. Data cleaning (ie. removing missing values) should be done prior to this step and done in R. Data cleaning in R means you’ll have a record of how the data was changed.

data science cycle from R for Data Science

From the chart above, we can see that data visualization is also an important step to understanding your data. The rest of this module will be spent exploring a new data set using the skills we have already covered, and building on them to create plots of the data.

Loading data from a package

We’ll explore the flights data in the data package called nycflights13. The flights object contains airline on-time data for all flights leaving airports in the New York City, NY area in 2013.

You will most likely have to install this package by using the RStudio GUI or install.packages() command, as we learned yesterday.

install.packages("nycflights13") #install package
library(nycflights13) #load library

You’ll notice the nycflights13 package includes other metadata:

airlines
airports
planes
weather

You can access them through the package using double colons following the package name (nycflights13::), but they are also loaded in the workspace automatically.

You’ll explore the data as a team of two, a driver and navigator. The driver will type the code, while the navigator checks for errors, and suggests answers. A good navigator will troubleshoot syntax questions by reading manual pages, googling, etc. Throughout the exercise you will be asked to switch roles with your teammate.

Your challenge

Your data exploration should be working towards describing the broad trends in the data, along with answering specific questions. You should work with your partner to develop a common set of goals. If time allows, you’ll present your findings to the clinic.

Data exploration might include answering the following:

Exploring data structure
- What is the data structure? columns and rows?
- How many total flights, total flights per airport or airline carrier?
- What are the different flight destinations?
- etc.
Exploring data with summary statistics
- What is the max, min and mean in flight delays? How does this break down by airline, airport or both?
- What is the most common flight destination? Least common?
- What is the average number of flights per month?
- Other descriptive statistics built into R include: mean, sd, var, min, max, median, range, and quantile
Exploring data with basic visualizations
- scatter plot: How does flight delay change with time? with weather? Do these relationships change with airport?
- histogram: What is the distribution of flights with time? to a destination?
- boxplot: What is the distribution of flight delay by airline?
- etc.

Practice: Get started by opening the manipulating_data.R script.

5. Data Visualization

This module will cover:

plotting in base R
plotting in ggplot

which will require the following skills already covered:

reading in data
manipulating data
assigning an object

We will also touch on choosing an appropriate visualization, interactive graphics, and maps.

Introduction

Data visualization in R can be quick and dirty (ie. data exploration for yourself) or highly polished (ie. communicating to others). We have already touched on quick data exploration in the third module yesterday. Today we will cover content to produce a more polished looking plot.

Two approaches to the same problem: Base `R` vs `ggplot`

Plotting in base R can allow the user to create highly customized plots. This customization takes time, and requires many decisions. An alternative is to use the package ggplot2 developed by Hadley Wickham based on the Grammar of Graphics written by Leland Wilkinson. ggplot2 has its own unique syntax that is a bit different from base R. I will walk through an example using base R and then recreate the figure using ggplot2. For even more side-by-side examples, see Nathan Yau’s blog post on Flowing Data.

Base `R`

A simple plot can take many more lines of code than you expect based on the visualization. When plotting in base R you’ll use a handful of parameter settings in either par() or in the plotting related functions listed below.

Important parameters

pch: plotting symbol
lty: line type
lwd: line width
col: plotting color
las: orientation of axis labels
bg: background color
mar: margin size
oma: outer margin size
mfrow: number of plots per row, column. Plots filled in row-wise.
mfcol: number of plots per row, column. Plots filled in column-wise.

Important functions

plot: make scatterplot
lines: add lines to plot
points: add points to plot
text: add text
title: add title to axes or plot
mtext: add margin text
axis: add axis tick/labels

Let’s create a plot of the total population by county area for 5 midwest states (example taken from Selva Prabhakaran’s tutorial). This data is part of the ggplot2 package. I start with the basic scatterplot function plot() and then customize from there.

library(ggplot2) #load the package with the data
data("midwest", package = "ggplot2") #load the data, midwest is now in the working environment. 
plot(y=log10(midwest$poptotal), x=midwest$area, #call the x and y values 
     col=as.factor(midwest$state), #point colors should be based on state 
     pch=19, cex=.75,#point shape and size
     ylim=c(3,7), xlim=c(0,.1), #set the axis limites
     las=1, #rotate the axis labels 
     xlab="Area", ylab=expression('Log'[10]*'(Total population)'),#label the axis
     main ="Area vs population"#add a title
     )

Legends and more

This is where the true power of plotting with base R customization shows. You can change the axis ticks and lables, add text anywhere, and even create multiple figures in a single visualization. The most common addition to any visualization will be the legend since they are not automatically created when plotting with base R. You have to add them manually. There are a few different methods to do this, but the function legend() works in most cases. To add the legend to the plot above, run the legend() function following the plot() function.

legend("topright", col=c(1:5), pch=19,legend=levels(as.factor(midwest$state)))

The visualization would then look like this:

A quick note on multipanel plots

A grid of plots in base R can be created using parameter setting mfrow or cfrow. Base R also gives you the option to make inset or subplots like this example here where the boxplot is inside the histogram.

x <- rnorm(100,sd=0.5)  #generate random data to plot
y <- rbinom(100, 1, 0.5) #generate random data to plot
par(fig = c(0,1,0,1)) #set dimensions of histogram figure from bottom, left, top, and right

hist(x)  #plot main figure

par(fig = c(0.07,0.35, 0.5, 1), new = T) #set dimensions of inset plot  
boxplot(x ~ y) #plot inset

The layout() function allows the user to create multipanel plots of different sizes, like this:

# One figure in row 1 and two figures in row 2
# row 1 is 1/3 the height of row 2
# column 2 is 1/4 the width of the column 1 
attach(mtcars)
layout(matrix(c(1,1,2,3), 2, 2, byrow = TRUE), 
    widths=c(3,1), heights=c(1,2))
hist(wt)
hist(mpg)
hist(disp)

Here is an example of figure that Reni made using base R that has lots of information layered into a single visualization.

If you’re interested in other customizations in base R check out Paul Murrell’s R Graphics book.

ggplot

The same exact scatterplot of county area vs populations size can be made using ggplot. Here the legend is automatically created. Check out the source of the example, which also has a compiled list of 50 different visualizations along with the code here.

For more detailed examples, check out the R Graphics Cookbook by Winston Chang.

# install.packages("ggplot2")
# load package and data
library(ggplot2)
theme_set(theme_bw())  # pre-set the bw theme.
# midwest <- read.csv("http://goo.gl/G1K41K")  # bkup data source

# Scatterplot
gg <- ggplot(midwest, #data, every arguement after this is connected with a '+' instead of a ','
             aes(x=area, y=log10(poptotal))) + #set the x and y col in data 
            geom_point(aes(col=state)) + #put a point at the (x,y) value, color it by state col
            xlim(c(0, 0.1)) + #set x axis limits
            labs( #name the different parts of the plot 
              subtitle="Area vs Population", 
              y="Population", 
              x="Area", 
              title="Scatterplot", 
              caption = "Source: midwest") 

plot(gg) #plot the object

ggplot also allows you to use facets, where you have several panels composing one plot. We will not cover these in particular today. But here is a plot that Ana made using facets.

plotly: easy interactive plots with ggplot

The plotly package is an add on to ggplot2 for quick interactive plots. The package is still relatively new and is under current development. The legends or other features are often poorly displayed but the interactive feature maybe useful for data exploration during an inperson meeting.

Below is an example from the plotly website. You’ll notice the syntax is similar to ggplot but the functions have changed a bit.

library(plotly)

p <- plot_ly(data = iris, x = ~Sepal.Length, y = ~Petal.Length,
        marker = list(size = 10, color = 'rgba(255, 182, 193, .9)', line = list(color = 'rgba(152, 0, 0, .8)', width = 2))) %>%
  layout(title = 'Styled Scatter', yaxis = list(zeroline = FALSE), xaxis = list(zeroline = FALSE))

p #plot the interactive graphic

plot_ly(z = volcano, type = "surface") #simple example of 3D surface plot

The googleVis package also has some great plots with tooltips built in.

Animated plots

The plotly package also allows for quick animations like this. Shiny is an easy introductory tool to more novel data visualizations.

Note: The code below will only work once you install ffmpeg, ImageMagick, or other such drivers. See the animation package documentation for more details.

suppressMessages(library(gganimate))
birth<-read.csv("birth.csv", sep='', header=TRUE)

pal <- c("#313695","#4575b4","#74add1","#abd9e9","#e0f3f8","#ffffbf","#fee090","#fdae61","#f46d43","#d73027","#a50026")
vals <- seq(10,32, length = 11)
birth <- ggplot(birth, aes(x = Year, y = BirthRate, frame = Year, cumulative = TRUE)) +
  geom_line(colour="black") +
  geom_point(shape = 21, colour="black", aes(fill=BirthRate), size=5, stroke=1) +
  scale_x_continuous(limits=c(1880,2015)) +
  scale_y_continuous(limits=c(10,32)) +
  theme_minimal() +
  scale_fill_gradientn(colors = pal, values = vals, rescaler = function(x, ...) x, oob = identity, guide=FALSE) +
  xlab("Year") +
  ylab("Birth rate") 
p<-gganimate(birth, "birth.gif", ani.width = 750, ani.height = 500, interval = 0.1)

Netherlands birth rate

Spatial data

Just like other data visualizations, mapping in R can be done a few different ways. Common packages include:

maps
rMaps
mapdata
ggmap
choroplethr
raster
sp
rgdal

The last 3 (raster, sp, and rgdal) are also useful for analyzing spatial data.

The choroplethr package is useful for plotting U.S. county level data like this:

#install.packages("choroplethr")
#install.packages("choroplethrMaps")
#install.packages("mapproj")
library(ggplot2)
library(choroplethr)
library(choroplethrMaps)
library(mapproj)

data(df_county_demographics)
df_county_demographics$value = df_county_demographics$percent_hispanic
county_choropleth(df_county_demographics, 
                  state_zoom = "texas",
                  title      = "Texas County Percent Hispanic 2012 Estimates",
                  num_colors = 9) + coord_map()

Newer packages like googleVis also have built-in interactive features.

suppressMessages(library(googleVis))
require(datasets)
states <- data.frame(state.name, state.x77)
GeoStates <- gvisGeoChart(states, "state.name", "Population",
                          options=list(region="US", 
                                       displayMode="regions", 
                                       resolution="provinces",
                                       width=600, height=400))
print(GeoStates,'chart')

Graphics for communication

There are plenty of guides on how to create the “best” visualization. This diagram is a good place to start when choosing your data visualizations.

Visualization Groups by Dr. Andrew Abela

If you’re plotting data to communicate (which is normally the case), some things you should keep in mind:

every addition plot feature is adding additional information
color choice (connotation, color blind)
how the audience expects to see data

For more details see Ten guidelines for effective data visualization in scientific publications by Kelleher and Wagener, 2011. At some point during your graduate career, you’ll likely hear about Edward Tufte’s philosophy on maximizing function over aesthetics.

6. Simulating Data

This module will cover:

simulating data of discrete model
simulating data of continuous model

which will require the following skills already covered:

function syntax
data structure
assigning an object
plotting in base R
plotting in ggplot
manipulating data

Mathematical models

Mathematical or dynamical models are abstract models that uses mathematical language to describe the behavior of a system

Logistic growth

A common model of population growth, originally proposed by to Pierre-François Verhulst in 1838, where the rate of reproduction is propoportional to both the existing population and the amount of available resources, all else being equal

The logistic model discrete

\[n(t+1) = n(t) + r_d n(t) \left(1-\frac{n(t)}{K}\right)\]

Where \(n(t+1)\) is new population size, \(r\) is the growth rate, \(K\) is the carrying capacity.

How do we solve this in R

disc.logistic = function(n, p) { ## here are just saying that 'disc.logistic' is a function that takes two arguments
  r = unname(p['r']) ## set the growth rate (dropping the parameter name with 'unname')
  K = unname(p['K']) ## set the carrying capacity
  n1 = n + r * n * (1 - n / K) ## calculate the new population size
  return(n1) ## and return it 
}

Practice: Get started by opening the Discrete_Model.R script

The logistic model continuous

In continuous models, we will explore a specific type of model: ordinary differential equations. These describe the rate at which variables changes over time

\[\frac{dN}{dt} = "function" N(t)\]

Where \(N(t)\) is the value of a (continuous) variable at time.

Here time is the independent variable and population size (\(N(t)\)) is the dependent variable.

If we plot as a function of time, then the slope of the curve would be \(\frac{dN}{dt}\). If the variable is increasing over time, the slope is positive; if it is decreasing, then it is negative.

We will need to numerically integrate the growth rate equation from time \(t=0\) to time \(t=T\)

The LSODA adaptive step size solver in R is a powerful algorithm because it can automatically adjust its step size according to how rapidly the solution is changing.

require(deSolve) ## the packge we will uuse for this simulation

#The LSODA function takes in four (non-optional) arguments

out <- lsoda(nstart, times, func, params)

So the Logistic model in continuous time looks like this:

\[\frac{dn(t)}{dt} = r_c n(t) \left(1-\frac{n(t)}{K}\right).\]

How do we solve this in R

cont.logistic = function(n, p) { ## here are just saying that 'm.logistic' is a function that takes two arguments
  r = unname(p['r']) ## set the growth rate (dropping the parameter name with 'unname')
  K = unname(p['K']) ## set the carrying capacity
   ## calculate the rate of change
  dndt = r * n * (1 - n / K)
  ## return the rate of change as a list object (required by ode)
  list(c(dndt)) ## if you were calculating more than one derivative, you would have c(dn1dt,dn2dnt,etc.)
}

Practice: Get started by opening the Continuous_Model.R script

SIR model

Epidemiological processes (e.g., infection of susceptible individuals, recovery of infected individuals). We will represent these with equations.

The classical \(SIR\) compartmental model tracks the proportions of the population in each of three classes (susceptible, denoted by \(S(t)\) , infectious \(I(t)\) and recovered \(R(t)\)). Here the variables of interest are susceptible, infectious and recovered individuals. As the epidemic progresses, these quantities can change over time. The total population size does not change.

SIR model

Here, the boxes represent the \(S\), \(I\), \(R\) classes. From the flow diagram, we can write down how the state variables , and change according to the following system of differential equations:

\[\frac{dS}{dt} = -\lambda(I,t)S\]

\[\frac{dI}{dt} = \lambda(I,t)S-\gamma I\]

\[\frac{dR}{dt} = \gamma I\]

How do we solve this in R

SIRModel <- function (t, x, params) {   
  
  # Computes the rate of change of the variables S, I and R over time
  #
  # Args:
  #   t: vector of time points in the integration
  #   x: vector of variables in the differential equation
  #   params: vector of parameter values
  #
  # Returns:
  #   The rate of change of the variables S, I and R.
  
  
  S <- x[1]                               #create local variable S, the first element of x
  I <- x[2]                               #create local variable I
  R <- x[3]                               #create local variable R
  
  
  with(                                   #we can simplify code using "with"
    as.list(params),                   #this argument to "with" lets us use the variable names
    {                                  #the system of rate equations
      
      N <- S + I + R
      
      dS <- -beta*S*I*(1/N)      ### make sure susceptibles are removed here (i.e. -beta*S*I/N)
      dI <- beta*S*I*(1/N)-gamma*I
      dR <- gamma*I
      dx <- c(dS,dI,dR)                #combine results into a single vector dx
      list(dx)                         #return result as a list,
      #note order must be same as the state variables
    }
  )
}

IDEAS R Data Clinic

Ana Bento & Reni Kaul

August 18-19 2017

1. Data types

R Objects

Data types

Data Structure

Vectors

Matrices

Lists

Factors

Data frames

Useful functions

Going further

2. Writing a script

The importance of a script

Practice: We will do this exercise together…

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Practice: Open your script and run it!

Step 9

Practice: Create a README text file

Going further

3. Functions

What is a function

Practice: Let’s copy and paste them into the console

Example 1a: Simple function

Practice: Choose other sets of numbers

Practice: Create a function that will return the sum of 2 integers

Example 1b: Rounding function

Example 2a: Control statements if

Example 2b: Control statements if else

Practice: Uncomment and fill in a simple function with a nested if statement will print alternative outcomes

Example 2c: Control statements while

Example 3: for loop

Example 4: Random number generation

Example 5: Descriptive stats

Practice: Write a function to compute standard error of dat

Example 6: The apply function

Practice: How do you calculate the sum of each row using apply?

Example 7: The lapply function

Example 8: The sapply function

Going further

4. Manipulating & exploring data

Loading tabular data

Iterative process of data exploration

Loading data from a package

Your challenge

5. Data Visualization

Introduction

Two approaches to the same problem: Base R vs ggplot

Base R

Important parameters

Important functions

Legends and more

A quick note on multipanel plots

ggplot

plotly: easy interactive plots with ggplot

Animated plots

Spatial data

Graphics for communication

6. Simulating Data

Mathematical models

Logistic growth

The logistic model discrete

How do we solve this in R

Practice: Get started by opening the Discrete_Model.R script

The logistic model continuous

How do we solve this in R

Practice: Get started by opening the Continuous_Model.R script

SIR model

How do we solve this in R

Practice: Get started by opening the SIR_Deterministic.R script

`R` Objects

Two approaches to the same problem: Base `R` vs `ggplot`

Base `R`